Fundamentals
The core facts every aspirant should own — each a titled nugget with a real-world story, the concept in plain words, and a memory trick. Works even when the internet doesn't.
1,200 fundamentals
“Brakes do negative work, draining a car's kinetic energy into heat until it stops.”
The net work done on a body equals its change in kinetic energy.
W = ΔKE
Memory trick: Net work = change in KE.
“Water held behind a dam is stored energy waiting to become electricity.”
Stored energy of position: gravitational PE = mgh near Earth.
PE = mgh
Memory trick: Height stores energy.
“A pendulum trades height for speed and back, forever (without friction).”
Energy can't be created or destroyed, only transformed; total energy stays constant.
Memory trick: Energy changes form, never vanishes.
“Two lifts reach the top floor; the more powerful one just gets there faster.”
Power is the rate of doing work, P = W/t = Fv.
P = W/t = Fv
Memory trick: Same work, faster = more power.
“Billiard balls click almost elastically; a crash where cars crumple is inelastic.”
Both conserve momentum; only an elastic collision also conserves kinetic energy.
Memory trick: Elastic keeps KE; inelastic loses it to heat.
“You push a door at its handle, not near the hinge — more distance, more turn.”
Torque τ = force × perpendicular distance is the turning effect of a force.
τ = rF sinθ
Memory trick: Torque = force × lever arm.
“A tightrope walker's long pole spreads mass out, making rotation sluggish and balance easier.”
Rotational 'mass' — resistance to angular acceleration; depends on how mass is distributed about the axis.
I = Σmr²
Memory trick: Mass far from axis counts a lot (distance squared).
“A skater pulls their arms in, shrinks I, and spins faster — conserving L.”
With no external torque, angular momentum L = Iω is conserved.
L = Iω
Memory trick: Pull in → spin faster.
“A solid cylinder beats a hollow one down a ramp — less energy 'wasted' spinning.”
A rolling body has both translational (½mv²) and rotational (½Iω²) kinetic energy.
KE = ½mv² + ½Iω²
Memory trick: Rolling = moving + spinning energy.
“The same law that drops an apple holds galaxies together.”
Every two masses attract with F = Gm₁m₂/r².
F = Gm₁m₂/r²
Memory trick: Inverse-square: double distance, quarter force.
“You'd weigh slightly less on a mountaintop than at sea level.”
g = GM/R² at a planet's surface; it weakens with altitude and depth.
g = GM/R²
Memory trick: g depends on the planet, not on you.
“Rockets must hit ~40,000 km/h to leave Earth for good.”
The minimum speed to break free of a planet's gravity; ≈ 11.2 km/s for Earth.
v = √(2GM/R)
Memory trick: Escape = √2 × orbital speed.
“The ISS orbits at ~7.8 km/s — forever 'falling' around Earth.”
Speed needed to stay in a circular orbit, v = √(GM/r).
v = √(GM/r)
Memory trick: Faster orbit = lower altitude.
“Outer planets crawl; Neptune takes 165 Earth-years for one lap of the Sun.”
The square of a planet's orbital period is proportional to the cube of its orbit radius (T² ∝ r³).
T² ∝ r³
Memory trick: Farther planet → much longer year.
“Gravity in orbit is still ~90% of surface gravity — they're just falling around the Earth.”
Astronauts float because they and their spacecraft are in continuous free fall together, not because gravity is absent.
Memory trick: Free fall = apparent weightlessness.
“Your ears hurt at the bottom of a swimming pool because water pressure grows with depth.”
Pressure increases with depth: P = P₀ + ρgh.
P = P₀ + ρgh
Memory trick: Deeper = higher pressure.
“A car hydraulic lift raises tonnes with a gentle push — pressure shared across a big piston.”
Pressure applied to an enclosed fluid is transmitted equally in all directions.
Memory trick: Small force, big area → big force.
“A steel ship floats because its hull displaces enough water to match its weight.”
A submerged body feels an upward buoyant force equal to the weight of fluid it displaces.
Memory trick: Buoyancy = weight of fluid pushed aside.
“Aeroplane wings lift because air rushes faster over the top, lowering the pressure there.”
In a flowing fluid, faster flow means lower pressure.
P + ½ρv² + ρgh = const
Memory trick: Fast flow = low pressure.
“Water striders walk on ponds and droplets pull into spheres because of surface tension.”
The 'skin' on a liquid caused by cohesive forces pulling surface molecules inward.
Memory trick: Liquids minimise their surface.
“Honey pours slowly and water quickly — honey is far more viscous.”
A fluid's internal friction resisting flow.
Memory trick: Thick fluid = high viscosity.
“Stretch a spring gently and it springs back; pull too far and it stays bent.”
Within the elastic limit, stress is proportional to strain.
stress ∝ strain
Memory trick: Small stretch → restoring force ∝ stretch.
“Steel has a huge Young's modulus — that's why it barely stretches under load.”
A measure of a solid's stiffness: stress divided by longitudinal strain.
Y = stress/strain
Memory trick: Higher modulus = stiffer material.
“A child on a swing, a guitar string, a vibrating atom — all sing the SHM song.”
Oscillation where the restoring force is proportional to and opposite the displacement (F = −kx).
F = −kx
Memory trick: Force pulls back ∝ how far you pushed.